surface vertices

Examples of surface vertices in the following topics:

• Polarization By Scattering and Reflecting

  • When light hits a reflective surface, the vertically polarized aspects of that light are refracted at that surface.
  • To better remember this, we can think of light as an arrow and the reflective surface as a target.
  • If the arrow hits the target perpendicularly (vertically polarized), it is going to stick in the target (be refracted into the surface).
  • Unpolarized light has equal amounts of vertical and horizontal polarization.
  • After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized.

• Surface Tension

  • Surface tension is the tendency of a liquid surface to resist forces applied to it.
  • Where the surfaces meet, forces must be in equilibrium.
  • In both cases, the vertical component of the surface tension is enough to support the weight of the object.
  • The leaf is a hydrophobic surface.
  • Summarize the cause for different surface tensions at a liquid's surface

• Banked and Unbacked Highway Curves

  • The components of the normal force $N$ in the horizontal and vertical directions must equal the centripetal force and the weight of the car, respectively.
  • In cases in which forces are not parallel, it is most convenient to consider components along perpendicular axes—in this case, the vertical and horizontal directions.
  • (A frictionless surface can only exert a force perpendicular to the surface—that is, a normal force. ) These two forces must add to give a net external force that is horizontal toward the center of curvature and has magnitude $\frac{mv^2}{r}$.
  • Because the car does not leave the surface of the road, the net vertical force must be zero, meaning that the vertical components of the two external forces must be equal in magnitude and opposite in direction.
  • From the figure, we see that the vertical component of the normal force is $N\cos\theta$, and the only other vertical force is the car's weight.

• Vertical Structure

  • The pressure gradient in the disk must resist the vertical component of gravity.
  • To determine how the thickness varies with radius we can use the various scalings in the first equation and assume that the temperature is given by the effective temperature of the surface.
  • This is essentially assuming that the disk is isothermal vertically.
  • The relative thickness of the disk remains nearly constant with radius if only internal heating is important in a vertically isothermal disk.
  • Because the gas in the central plane of the disk can only be hotter than at the surface, the thickness estimated in this manner is a lower limit.

• Key Points: Range, Symmetry, Maximum Height

  • It is the time from when the object is projected to the time it reaches the surface.
  • All projectile motion happens in a bilaterally symmetrical path, as long as the point of projection and return occur along the same horizontal surface.
  • Bilateral symmetry means that the motion is symmetrical in the vertical plane.
  • This is also the point where you would draw a vertical line of symmetry.
  • There is no acceleration in this direction since gravity only acts vertically. shows the line of range.

• Pressure

  • where p is pressure, F is the force acting perpendicular to the surface to which this force is applied, and A is the area of the surface.
  • The magnitude of the pressure exerted by an object on a given surface is equal to its weight acting in the direction perpendicular to that surface, divided by the total surface area of contact between the object and the surface. shows the graphical representations and corresponding mathematical expressions for the case in which a force acts perpendicular to the surface of contact, as well as the case in which a force acts at angle θ relative to the surface.
  • Since pressure depends only on the force acting perpendicular to the surface upon which it is applied, only the force component perpendicular to the surface contributes to the pressure exerted by that force on that surface.
  • It has an area of contact (with the surface upon which it is resting) of 0.1 m2, thus exerting a pressure of 1,000 Pa on that surface.
  • That same block in a different configuration (also in Figure 2), in which the block is placed vertically, has an area of contact with the surface upon which it is resting of 0.01 m2, thus exerting a pressure of 10,000 Pa—10 times larger than the first configuration due to a decrease in the surface area by a factor of 10.

• Portals of Microbe Entry

  • Microbes gain access to human tissues via mucosal surfaces within the body or epithelial surfaces on the outside of the body.
  • direct physical contact (usually by touching soil contamination or a contaminated surface)
  • Disease can also be directly transmitted in two ways: horizontally or vertically.
  • Vertical disease transmission involves passing a disease causing agent vertically from parent to offspring.
  • Recognize the various methods and types of microorganism transmission: vectors, hosts, horizontal, vertical transmissions

• Constant Acceleration

  • Analyzing two-dimensional projectile motion is done by breaking it into two motions: along the horizontal and vertical axes.
  • The components of acceleration are then very simple: $a_y = -g = -9.81 \frac{m}{s^2}$ (we assume that the motion occurs at small enough heights near the surface of the earth so that the acceleration due to gravity is constant).
  • Because the acceleration due to gravity is along the vertical direction only, $a_x = 0$.
  • The velocity in the vertical direction begins to decrease as an object rises; at its highest point, the vertical velocity is zero.
  • As an object falls towards the Earth again, the vertical velocity increases again in magnitude but points in the opposite direction to the initial vertical velocity.

• Steel-Frame Construction

  • Steel frame construction is a building technique in which vertical steel columns and horizontal I-beams form a 'skeleton frame'.
  • Steel frame usually refers to a building technique with a 'skeleton frame' of vertical steel columns and horizontal I-beams, constructed in a rectangular grid to support the floors, roof, and walls of a building which are all attached to the frame.
  • The horizontal elements of the "I" are flanges, while the vertical element is termed the 'web'.
  • Often in office buildings, the final floor surface is provided by some form of raised flooring system with the void between the walking surface and the structural floor being used for cables and air handling ducts.

• Fischer Projection Formulas

  • The problem of drawing three-dimensional configurations on a two-dimensional surface, such as a piece of paper, has been a long-standing concern of chemists.
  • In a Fischer projection drawing, the four bonds to a chiral carbon make a cross with the carbon atom at the intersection of the horizontal and vertical lines.
  • The two vertical bonds are directed behind the central carbon (away from the viewer).
  • Note that it is customary to set the longest carbon chain as the vertical bond assembly.
  • If the lowest priority group (often a hydrogen) is on a vertical bond, the configuration is given directly from the relative positions of the three higher-ranked substituents.